I'm not thrilled with this possibility. I tend to bring my own toiletries, but I like having the hotel's as a backup. Sometimes it's even from a brand I like, which is always a nice surprise. It appears cheap on Disney's part not to provide the mini bottles, there is a reason this has only happened in the values before (which I've stayed in, lest someone think me a snob). I'm sure they will try to pass it off as a green initiative. Disney likes being green when it saves them money. It seems gross, but I don't know if it would actually cause illness.
I'm also a germaphobe. There's only so much you can do, though. I touch sink handles with paper towels or my elbow. I don't use the hand dryers. I don't touch bathroom door handles when I'm exiting. I'm not going to go so far as to not use a soap dispenser because it's not perfectly clean. Using hand sanitizer instead is inconsiderate to others because it does not kill most of the germs you need it to from a bathroom trip.
When going to a hotel, theme park, the gym, the mall, etc. I think about germs more than most people, but I try to draw the line at what I consider reasonable precautions. So, things like hand washing before a meal if I've been touching things like lap bars, ticket readers, etc. Wiping down a mat at the gym before I use it and removing the decorations from the bed at a hotel are some things I do. I'm not going to not use the hotel couch though or bring Clorox wipes to wipe down things. I can't make everything clean, even though I totally want to. Everyone has their comfort level and as long as it's not putting other people at risk (like the hand sanitizer example), have at it.